On the spread of outerplanar graphs

Abstract

The spread of a graph is the difference between the largest and most negative eigenvalue of its adjacency matrix. We show that for sufficiently large nn, the nn-vertex outerplanar graph with maximum spread is a vertex joined to a linear forest with Ω(n)\Omega \left(n) edges. We conjecture that the extremal graph is a vertex joined to a path on n−1n-1 vertices.

Keywords

• spread
• adjacency eigenvalues
• outerplanar
• 05c50